Extremal solutions of fuzzy fractional Volterra integral equations involving the generalized kernel functions by the monotone iterative technique

Article type: Research Article

Authors: Vinh An, Truong^a | Van Hoa, Ngo^{b; c; *}

Affiliations: [a] Faculty of Applied Sciences, University of Technology and Education, Ho Chi Minh City, Vietnam | [b] Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam | [c] Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Correspondence: [*] Corresponding author. Ngo Van Hoa, Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam. E-mail: ngovanhoa@tdtu.edu.vn.

Abstract:  In this work, we consider a new form of fuzzy fractional Volterra integral equations (FFVIEs) involving the generalized kernel functions. By using the monotone iterative technique (MIT) combined with the method of lower and upper solutions, the existence of extremal solutions of FFVIEs is established. Some examples are given to illustrate our main results.

Keywords: Fuzzy fractional integral equations, generalized kernel functions, extremal solutions, monotone iterative technique

DOI: 10.3233/JIFS-191746

Journal: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 4, pp. 5143-5155, 2020